Vertex count increases drastically when exporting to .FBX
I would generally blame the fact that many programs hate quads (not without reason; graphics cards usually only use tris, so it splits them into tris, regardless). However, that shouldn't change your vertex count so drastically since it's only changing face count, and should retain the same number of vertices. It seems likely, then, that you have some sort of modifier in place, subsurf is the usual suspect, that hasn't been applied. Try applying all your modifiers before exporting, and see if this solves your issue.